Breit Equation with Form Factors in the Hydrogen Atom

Abstract

The Breit equation with two electromagnetic form-factors is studied to obtain a potential with finite size corrections. This potential with proton structure effects includes apart from the standard Coulomb term, the Darwin term, retarded potentials, spin-spin and spin-orbit interactions corresponding to the fine and hyperfine structures in hydrogen atom. Analytical expressions for the hyperfine potential with form factors and the subsequent energy levels including the proton structure corrections are given using the dipole form of the form factors. Numerical results are presented for the finite size corrections in the 1S and 2S hyperfine splittings in the hydrogen atom, the Sternheim observable $D_{21}$ and the 2S and 2P hyperfine splittings in muonic hydrogen. Finally, a comparison with some other existing methods in literature is presented.

24 pages, Latex, extended version, title changed

References in corpus (8)

• Nucleon Electromagnetic Form Factors
• Electromagnetic form factors of the nucleon: new fit and analysis of uncertainties
• New Measurement of the 2S Hyperfine Interval in Atomic Hydrogen
• Parity violation in hydrogen revisited
• Neutron structure effects in the deuteron and one neutron halos
• Breit type equation for mesonic atoms
• A new approach to the relativistic treatment of the fermion-boson system, based on the extension of the SL(2,C) group
• A new two-body relativistic potential model for pionic hydrogen

Cited by in corpus (6)

• Model independent extraction of the proton magnetic radius from electron scattering
• Non-perturbative evaluation of some QED contributions to the muonic hydrogen $\mathbf{n}=2$ Lamb shift and hyperfine structure
• Determining the size of the proton
• Relativistic corrections to the thermal interaction of bound particles
• Coulomb Law in the Non-Uniform Euler-Heisenberg Theory
• Short Range Interactions in the Hydrogen Atom